Problem: Simplify the following expression: $ n = \dfrac{-9x - 1}{-5x - 9} + \dfrac{-9}{2} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{-9x - 1}{-5x - 9} \times \dfrac{2}{2} = \dfrac{-18x - 2}{-10x - 18} $ Multiply the second expression by $\dfrac{-5x - 9}{-5x - 9}$ $ \dfrac{-9}{2} \times \dfrac{-5x - 9}{-5x - 9} = \dfrac{45x + 81}{-10x - 18} $ Therefore $ n = \dfrac{-18x - 2}{-10x - 18} + \dfrac{45x + 81}{-10x - 18} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{-18x - 2 + 45x + 81}{-10x - 18} $ $n = \dfrac{27x + 79}{-10x - 18}$ Simplify the expression by dividing the numerator and denominator by -1: $n = \dfrac{-27x - 79}{10x + 18}$